Methods and apparatus for use in reducing residual phase error in OFDM communication signals

ABSTRACT

Methods and apparatus for use in reducing residual phase error (RPE) in orthogonal frequency division multiplexed (OFDM) communication signals are described. In at least one embodiment of the invention, an apparatus includes a residual phase error estimator configured to estimate a residual phase error at least partially based on a plurality of phases of a first channel-compensated received signal and a plurality of phases of a sliced version of the first channel-compensated received signal. The residual phase error estimator is configured to correct a channel estimate at least partially based on the residual phase error estimate to thereby generate a corrected channel estimate. The apparatus includes a channel compensator configured to generate a second channel-compensated received signal at least partially based on a received signal and the corrected channel estimate.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. patent application Ser. No.11/167,385, filed Jun. 27, 2005, entitled “Methods and Apparatus for Usein Reducing Residual Phase Error in OFDM Communication Signals,” naminginventor Hongliang Zhang, which application is a continuation of U.S.patent application Ser. No. 09/670,286, filed Sep. 25, 2000, (U.S. Pat.No. 6,928,120), entitled “Methods and Apparatus for Use in ReducingResidual Phase Error in OFDM Communication Signals,” naming inventorHongliang Zhang, which are both incorporated herein in their entirety.

BACKGROUND

1. Field of the Invention

The present invention relates generally to the field of radiocommunication receivers. More particularly, the present inventionrelates to the field of reducing residual phase error (RPE) oforthogonal frequency division multiplexing (OFDM) signals in OFDMcommunication receivers.

2. Description of the Related Art

An increasing need for broadband mobile/fixed wireless communicationsservices has motivated researchers and radio engineers to search for avariety of feasible radio airlink interface techniques for such wirelesscommunication systems. An airlink interface technique based on theOrthogonal Frequency Division Multiplexing (OFDM) modulation isconsidered an attractive candidate for a broadband wireless transmissionsystem due to its spectral efficiency, its robustness in differentmultipath propagation environments and its ability to combat intersymbolinterference (ISI).

OFDM is a multi-carrier modulation method. It divides an entirefrequency band into many, say N, subchannels or frequency tones, andeach subchannel is modulated with a constellation symbol to betransmitted. In its application as a multiple access method for apoint-to-multipoint wireless communication system, OFDM arranges thesetotal N subchannels as follows. M adjacent subchannels are groupedtogether (where M<<N) without overlapping between adjacent groups. Eachmobile user is assigned a cluster of M subchannels when it needs totransmit information data between its serving base station and itsterminal. In each cluster of M subchannels assigned to an individualuser, one or more subchannels may be used to transmit pilot signals andare called “pilot subchannels.” The rest of the subchannels bearinformation data and are called “information subchannels.” For anavailable bandwidth of B MHz, there are a total of N subchannels with afrequency space of B/N MHz; this band can simultaneously support N/Musers.

An OFDM-based wireless system, however, is very sensitive to channelphase errors and the phase noise of the receiver local oscillator (LO).Therefore, an effective fading channel estimation and the transformdomain channel compensation become necessary to restore OFDM signalorthogonality, to correct phase error, and to conduct coherentdemodulation in the receiver.

Pilot symbol-aided approaches are widely used to estimate the fadingchannel properties which corrupt the transmitted signal. In an OFDM/TDMAsystem, an OFDM data block is the block of M constellation symbols to betransmitted within a TDMA time slot. When the transmission channel orphase noise changes significantly from one OFDM data block to the next,channel estimation and transform domain channel compensation must beperformed in each individual data block with the pilot symbols insertedin the given data block. For example, the interval between two OFDM datablocks may be on the order of 3-5 milliseconds. In such a relativelylong time period, the phase noise effect of the receiver LO may changesignificantly.

Co-channel interference due to any frequency reuse pattern, multipathfading, and additive white Gaussian noise (AWGN) are primary constraintsto an acceptable performance in a cellular/wireless communicationsystem. In addition, intercarrier interference (ICI) due to channelvariation and phase noise always exists in an OFDM-based wirelesssystem. Thus, the pilot symbols as well as the information symbols arecorrupted by co-channel-interference, intercarrier-interference, noise,and other channel impairments. All of these impairments in the receivedpilot signals significantly affect the accuracy of the channelestimation. A residual phase error (RPE) is the phase error that remainsafter the received constellation symbols are compensated based on aninaccurate channel estimation.

With conventional techniques, the accuracy of the channel estimation maybe improved by either increasing the number of pilot signals and/orincreasing their transmission power. On one hand, using a larger numberof pilot symbols results in a higher transmission overhead and hence alower system capacity. On the other hand, a larger transmission powerfor pilot sub-channels results in larger ICIs for information-bearingtones and hence causes implementation difficulties. Accordingly, thereis an existing need to reduce the residual phase error in OFDMcommunication signals without the deficiencies of the prior art.

SUMMARY

Methods and apparatus for use in reducing the residual phase error (RPE)in OFDM communication signals are described. A pilot symbol-aidedchannel estimation scheme is employed in a wireless OFDM system. The newtechnique takes advantage of OFDM-based systems where a block ofconstellation symbols are transmitted simultaneously and all of thesesymbols experience the same channel fading. Broadly, the techniqueutilizes a block of detected symbols, based on their hard-decisions asthe real transmitted symbols, to estimate and remove the residual phaseerror after the channel has been compensated.

In at least one embodiment of the invention, an apparatus includes aresidual phase error estimator configured to estimate a residual phaseerror at least partially based on a plurality of phases of a firstchannel-compensated received signal and a plurality of phases of asliced version of the first channel-compensated received signal. Theresidual phase error estimator is configured to correct a channelestimate at least partially based on the residual phase error estimateto thereby generate a corrected channel estimate. The apparatus includesa channel compensator configured to generate a secondchannel-compensated received signal at least partially based on areceived signal and the corrected channel estimate.

In at least one embodiment of the invention, a method for use inorthogonal frequency division multiplexed (OFDM) communications includesestimating a residual phase error at least partially based on aplurality of phases of a first channel-compensated received signal and aplurality of phases of a sliced version of the first channel-compensatedreceived signal to thereby generate a residual phase error estimate. Themethod includes generating a second channel-compensated received signalat least partially based on the received signal and a corrected channelestimate. The corrected channel estimate is at least partially based onthe residual phase error estimate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a wireless communication system, such as a fixedwireless system utilizing orthogonal frequency division multiplexing(OFDM) communication techniques, which includes one or more base unitsand one or more remote units.

FIG. 2 is a general block diagram of processing components for anOFDM-based wireless communication system which utilizes pilot-basedsignal correction.

FIG. 3 is a block diagram of more specific processing components of theremote unit of FIG. 2 related to channel compensation using pilot tonesymbols.

FIG. 4 is a graph showing relationships between fading channel gain, itsestimation, and the estimation error for the channel compensationdescribed in relation to FIG. 3.

FIG. 5 is a block diagram of a first embodiment of components utilizedin the remote unit of FIG. 2 which are operative to reduce residualphase error in OFDM communication signals.

FIG. 6 is a block diagram of a second embodiment of components utilizedin the remote unit of FIG. 2 which are operative to reduce the residualphase error in OFDM communication signals.

FIG. 7 is a flowchart describing a method for use in reducing theresidual phase error in OFDM communication signals.

FIG. 8 is a timing diagram showing radio frequency (RF) OFDM signals andOFDM packets in the wireless communication system.

FIG. 9 is an illustrative representation of the relationship betweentime slots and time frames utilized in the wireless communicationsystem.

FIG. 10 is an illustrative representation of the frequency layout oftraffic and pilot tones utilized in the wireless communication system.

DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

FIG. 1 is an illustrative representation of a wireless communicationsystem 100 which utilizes orthogonal frequency division multiplexing(OFDM) or OFDM-like communication methodologies. Wireless communicationsystem 100 includes at least one base unit 106 having one or moreantennas 108, and a plurality of remote units 102 (“RUs” or “transceiverunits”), such as remote unit 104. Base unit 106 and remote units 102communicate via radio frequency (RF) signals, such as RF signals 110between base unit 106 and remote unit 104. Wireless communication system100 can make use of a number of different communication techniques, suchas frequency division multiple access (FDMA), time division multipleaccess (TDMA), or time division duplex (TDD).

Preferably, wireless communication system 100 is a “fixed wirelesssystem” (FWS) or Digital Broadband service, where base unit 106 providestelephone and high-speed data communication to each one of a number offixed-location subscribers equipped with an RU. Also, the RF OFDMcommunications signals are modulated using 16 quadrature amplitudemodulation (QAM), or quadrature phase shift keying (QPSK). Further, thewireless system employs a frequency division duplex (FDD) technique toimplement the downlink (base unit to remote unit) and uplink (remoteunit to base unit) transmissions. Since uplink and downlinktransmissions are symmetric, only downlink transmission will bedescribed herein.

Referring to FIG. 8, each base unit of the wireless communication systemtransmits a plurality of OFDM packets 802, such as an OFDM packet 804,to a corresponding remote unit. A new OFDM packet is transmitted onceevery predetermined time period. Each predetermined time period isassociated with a time slot, such as a time slot 906 of FIG. 9. Asindicated in FIG. 9, a plurality of consecutive time slots 904corresponds to a time frame 902. In the embodiment shown, each time slothas a duration of 375 microseconds, each OFDM packet is 320 microsecondsin length, and each time frame corresponds to 8 time slots for aduration of 3 milliseconds.

Each base unit transmits “traffic tones” and “pilot tones” to acorresponding remote unit. Traffic tones are utilized for thecommunication of voice and/or data, whereas pilot tones are utilized forchannel compensation. In general, each remote unit samples the OFDMwaveforms at a sampling rate to generate time domain samples, andconverts the time domain samples into frequency domain signals (e.g.,traffic or pilot tones). Referring to FIG. 10, an illustrativerepresentation of the frequency layout of traffic and pilot tonesutilized in the wireless communication system is shown. Data symbols ontraffic tones (“Tch”) of a particular frequency slot are transmitted ina particular time slot. For example, data symbols on traffic tones 1002of frequency slot 1006 are transmitted in one particular time slot. Asindicated in FIG. 10, each frequency slot has eighteen traffic tones.One or more of these tones, such as a tone 1004, are used as pilot tonesfor channel estimation and compensation.

Each remote unit is assigned a traffic channel that is defined by aunique time and frequency slot combination. One remote unit may beassigned to receive information within, for example, each time slot to(e.g., time slot 906 of FIG. 9) at frequency slot f₅ (e.g., a frequencyslot 1002 of FIG. 10), while another remote unit may be assigned toreceive information within, for example, each time slot t₆ at frequencyslot f₂. Each remote unit in the wireless communication system utilizesthe pilot tone within its assigned time slot to perform channelcompensation and the methods described herein. So, if a single pilottone is provided within each time slot, then each remote unit utilizes asingle pilot tone in each time frame for channel compensation.

FIG. 2 shows a general block diagram 200 of an OFDM-based radiocommunication system which utilizes pilot-based signal correction.Diagram 200 is divided into base unit processes 202 for a base unit,remote unit processes 204 for a remote unit, and an airlink 206. In baseunit processes 202, binary information data is encoded using a channelencoding process 208 and mapped into M−1 multi-amplitude multi-phaseconstellation symbols using a signal mapping process 210. In aserial-to-parallel conversion process 212 (“S/P”), one pilot symbol isinserted in the information data sequence for a “user i” before its datais multiplexed with other users' data. There are total M symbols foruser i. A data sequence of length N from K users is converted into Nparallel symbols, which are fed into an Inverse Fast Fourier Transform(IFFT) 214 from a tone mapping process 214. IFFT 214 modulates thesesymbols on N subcarriers and sums them. Next, a guard interval is addedby a guard interval insertion process 218 and a parallel-to-serialconversion process 220 (“P/S”) is applied. After digital-to-analog (D/A)conversion and filtering with a D/A converter and lowpass filter 222,the signals are upconverted to a carrier frequency and transmitted overairlink 206.

The signals over airlink 206 are received and processed by remote unitprocesses 204. After downconversion of the signals, lowpass filteringand analog-to-digital (A/D) conversion are applied using an A/Dconverter and lowpass filter 224. A serial-to-parallel conversionprocess 226 (“S/P”) converts the signals from serial to parallel and aguard interval removal process 228 removes the existing guard interval.Data for user i is demultiplexed from the output of a Fast FourierTransform (FFT) 230, where tone demapping is performed by a tonedemapping process 232. Pilot-based signal correction is performed usinga channel estimation process 234 and a signal correction process 236.Finally, M−1 information-bearing symbols are demapped and decoded intobinary data by a signal demapping process 240 and a channel decodingprocess 242, respectively.

A collection of M consecutive sub-carriers/tones, called thetransmission channel or link, is used to transmit M constellationsymbols in a parallel fashion. The selection of M is based on the datarate and fading environment: It is typically chosen so that the traffictransmission channel is frequency-flat and no channel equalizer isnecessary. Therefore, the transmission channel of M sub-channels isassumed as a frequency-flat channel.

FIG. 3 shows a receiver processing portion 300 of a remote unit inwireless communication system 100 of FIG. 1. Receiver processing portion300 includes a channel estimation process 302 and a channel compensationprocess 304. The following detailed signal model analysis is based onreceiver processing portion 300 shown in FIG. 3.

A block of M encoded and modulated constellation symbols to betransmitted, denoted as X(n), is

$\begin{matrix}{{X(n)} = \begin{bmatrix}{S_{1}(n)} \\{S_{2}(n)} \\\vdots \\{S_{M - 1}(n)} \\{S_{P}(n)}\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$where n is the index for the nth block of user data and each blockconsists of M symbols, one of them is the pilot symbol; S_(P)(n) is thepilot symbol inserted in the nth block of user data; and S₁(n), i=1, 2,3, . . . , M−1, are information-bearing symbols in the nth block ofdata.

Since the channel estimation and signal correction are conducted inevery individual OFDM data block, the block index n in the remainingdescription will be ignored. Therefore, we have

$\begin{matrix}\begin{matrix}{X = \begin{bmatrix}S_{1} \\S_{2} \\\vdots \\S_{M - 1} \\S_{P}\end{bmatrix}} \\{= \begin{bmatrix}X_{in} \\S_{P}\end{bmatrix}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$where the information-bearing data block, X_(in), is

$\begin{matrix}{X_{in} = {\begin{bmatrix}S_{1} \\S_{2} \\\vdots \\S_{M - 1}\end{bmatrix} = S}} & \left( {{Eq}.\mspace{14mu} 3} \right)\end{matrix}$

The transmission channel for an individual user is considered afrequency-flat fading channel and its transfer function is modeled as acomplex coefficient denoted as α(n). This is because the bandwidth whichM subchannels spans is much less than the fading channel coherentbandwidth.

The receiver local oscillator (LO) phase noise has two effects on theOFDM signal. One effect is the common phase errors that are the same forall subchannels. The common phase error is, in fact, a phase shift foreach subchannel and can be incorporated with fading channel phase. Thesecond effect is a noise-like intercarrier interference (ICI). It can betreated as noise, and will therefore not be considered in the remainingdescription.

At the receiver side, the received signal may be represented as

$\begin{matrix}{{r = {{\alpha \cdot X} + N}}{and}} & \left( {{Eq}.\mspace{14mu} 4} \right) \\{\begin{matrix}{r = \begin{bmatrix}r_{1} \\r_{2} \\\; \\\; \\r_{M - 1} \\r_{P}\end{bmatrix}} \\{= \begin{bmatrix}{{\alpha \cdot S_{1}} + n_{1}} \\{{\alpha \cdot S_{2}} + n_{2}} \\\; \\\; \\{{\alpha \cdot S_{M - 1}} + n_{M - 1}} \\{{\alpha \cdot S_{P}} + n_{P}}\end{bmatrix}} \\{= \begin{bmatrix}r_{in} \\r_{P}\end{bmatrix}}\end{matrix}{where}} & \left( {{Eq}.\mspace{14mu} 5} \right) \\{\begin{matrix}{r_{in} = \begin{bmatrix}r_{1} \\r_{2} \\{\;\vdots} \\\; \\r_{M - 1}\end{bmatrix}} \\{= \begin{bmatrix}{{\alpha \cdot S_{1}} + n_{1}} \\{{\alpha \cdot S_{2}} + n_{2}} \\{\vdots\;} \\\; \\{{\alpha \cdot S_{M - 1}} + n_{M - 1}}\end{bmatrix}} \\{= {{\alpha \cdot X_{in}} + N_{in}}}\end{matrix}{and}} & \left( {{Eq}.\mspace{14mu} 6} \right) \\\begin{matrix}{N = \begin{bmatrix}n_{1} \\n_{2} \\\vdots \\n_{M - 1} \\n_{P}\end{bmatrix}} \\{= \begin{bmatrix}N_{in} \\n_{P}\end{bmatrix}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 7} \right) \\{N_{in} = \begin{bmatrix}n_{1} \\n_{2} \\\vdots \\n_{M - 1}\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 8} \right)\end{matrix}$n_(i), i=1, 2, 3, . . . , M−1, and np are AWGN with a mean of zero and avariance of σ². The received pilot symbol, r_(P), isr _(P) =α·S _(P) +n _(P)  (Eq. 9)

Channel Estimation. Based on the received pilot symbol, r_(P), in Eq. 9and the previously known pilot symbol, S_(P), the channel transferfunction, α, in the nth OFDM data block can be estimated based on

$\begin{matrix}\begin{matrix}{\hat{\alpha} = \frac{S_{P}^{*} \cdot r_{P}}{{S_{P}}^{2}}} \\{= {\alpha + \frac{S_{P}^{*} \cdot n_{P}}{{S_{P}}^{2}}}} \\{= {\alpha + \alpha_{N}}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 10} \right)\end{matrix}$where α is the true fading channel gain or transfer function. Thechannel estimation error, α_(N), due to co-channel interference (CCI),AWGN, and ICI is

$\begin{matrix}{\alpha_{N} = \frac{S_{P}^{*} \cdot n_{P}}{{S_{P}}^{2}}} & \left( {{Eq}.\mspace{14mu} 11} \right)\end{matrix}$

Since S_(P) is a complex constant and its norm, ∥S_(P)∥², is a realconstant, the channel gain estimation error, α_(N), is an AWGN variablewith a mean of zero and variance of σ²/∥S_(P)∥². The mean-square-error(MSE) of the channel estimation method in Eq. 10 isMSE=σ ² /∥S _(P)∥²  (Eq. 12)

FIG. 4 depicts the relationships between true channel gain (at 402), itsestimate (at 404), and the estimation error (at 406). From FIG. 4, it isfound that the estimated fading channel gain, {circumflex over (α)}, canbe given by{circumflex over (α)}=(|α|+ζ)·e ^(j(φ+φ) ^(N) ⁾  (Eq. 13)where ζ is a random variable and its value is limited as−|α|≧ζ∞  (Eq. 14)and φ_(N) is a phase error variable within a small range. The φ_(N) isthe channel phase estimation error and it is called the residual phaseerror (at 408).

In Eq. 13, the real channel transfer function, α, in the nth OFDM blockdata, is treated asα=|α|e ^(jφ)  (Eq. 15)

Signal Correction/Channel Compensation. With the estimate of fadingchannel gain or transfer function in Eq. 13, the received informationbearing signals are corrected based on

$\begin{matrix}{{\hat{X}}_{in} = \frac{{\hat{\alpha}}^{*} \cdot r_{in}}{{\hat{\alpha}}^{2}}} & \left( {{Eq}.\mspace{14mu} 16} \right)\end{matrix}$Substituting r_(in) in Eq. 16 with the result in Eq. 6, Eq. 16 can besimplified as

$\quad\begin{matrix}\begin{matrix}{{\hat{X}}_{in} = \frac{{\hat{\alpha}}^{*} \cdot r_{in}}{{\hat{\alpha}}^{2}}} \\{= \frac{{\hat{\alpha}}^{*} \cdot \left( {{\alpha \cdot X_{in}} + N_{in}} \right)}{{\hat{\alpha}}^{2}}} \\{= {{\frac{\left( {{\hat{\alpha}}^{*} \cdot \alpha} \right)}{{\hat{\alpha}}^{2}} \cdot X_{in}} + \frac{{\hat{\alpha}}^{*} \cdot N_{in}}{{\hat{\alpha}}^{2}}}} \\{= {{\frac{\alpha }{\hat{\alpha}} \cdot {\mathbb{e}}^{{- {j\phi}}\; N} \cdot X_{in}} + \frac{{\hat{\alpha}}^{*} \cdot N_{in}}{{\hat{\alpha}}^{2}}}} \\{= {{\frac{\alpha }{{\alpha } + \zeta} \cdot {\mathbb{e}}^{{- {j\phi}}\; N} \cdot X_{in}} + \frac{{\hat{\alpha}}^{*} \cdot N_{in}}{{\hat{\alpha}}^{2}}}} \\{{\frac{1}{1 + \frac{\zeta}{\alpha }} \cdot {\mathbb{e}}^{{- {j\phi}}\; N} \cdot X_{in}} + S_{N}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 17} \right)\end{matrix}$where the second item of Eq. 17 is due to CCI, AWGN, and ICI presentedin information-bearing subchannels and it is given by

$\quad\begin{matrix}{\begin{matrix}{S_{N} = \frac{{\hat{\alpha}}^{*} \cdot N_{in}}{{\hat{\alpha}}^{2}}} \\{= {\frac{{\hat{\alpha}}^{*}}{{\hat{\alpha}}^{2}} \cdot \begin{bmatrix}n_{1} \\n_{2} \\\vdots \\n_{M - 1}\end{bmatrix}}} \\{= \begin{bmatrix}S_{N\; 1} \\S_{N\; 2} \\\vdots \\S_{{NM} - 1}\end{bmatrix}}\end{matrix}{and}} & \left( {{Eq}.\mspace{14mu} 18} \right) \\{{\hat{X}}_{in} = \begin{bmatrix}{\hat{X}}_{1} \\{\hat{X}}_{2} \\\vdots \\{\hat{X}}_{M - 1}\end{bmatrix}} & \left( {{Eq}.\mspace{14mu} 19} \right)\end{matrix}${circumflex over (X)}_(i), i=1, 2, 3, . . . , M−1 are estimates ofconstellation symbols transmitted over the fading channel using OFDMsignals. These estimated symbols are then demodulated and decoded to thebinary data.

Effect Of Channel Estimation Error, α_(N). An estimate for an individualsymbol in the nth data block is given as follows:

$\begin{matrix}\begin{matrix}{{\hat{X}}_{i} = {{\frac{1}{1 + \frac{\zeta}{\alpha }} \cdot {\mathbb{e}}^{{- {j\phi}}\; N} \cdot S_{i}} + S_{Ni}}} \\{= {{\frac{1}{1 + \frac{\zeta}{\alpha }} \cdot {\mathbb{e}}^{{- {j\phi}}\; N} \cdot S_{i}} + {\frac{{\hat{\alpha}}^{*}}{{\hat{\alpha}}^{2}} \cdot n_{i}}}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 20} \right)\end{matrix}$

The second item, S_(Ni), is an AWGN variable. Eq. 20 reveals that thechannel estimation error, α_(N), has two major effects on thetransmitted symbols, S_(i), i=1, 2, 3, . . . , M−1, in the nth block ofOFDM data.

The first effect is that the constellation of transmitted symbols isscaled by a factor of

$1/\left( {1 + \frac{\zeta}{\alpha }} \right)$instead of 1. If the channel estimation error is very small, or zero,then Eq. 20 becomes

$\begin{matrix}{{\hat{X}}_{i} = {S_{i} + {\frac{\alpha^{*}}{{\alpha }^{2}} \cdot n_{i}}}} & \left( {{Eq}.\mspace{14mu} 21} \right)\end{matrix}$However, if the channel estimation error is very large, or the channelgain, α, is so small that the whole OFDM block signal is in deep fadingand is immersed in the noise, the estimate, {circumflex over (α)}, ofthe channel gain, α, is almost zero and noise will only be obtained fromthe channel estimation and signal correction. Some diversities andcombining techniques may be used to effectively deal with such deepfading in a wireless communication system.

The second effect is that the constellation of the transmitted symbolsis rotated by an angle of φ_(N). Similarly, if the channel estimationerror is very small, then the residual angle will become small too. Botheffects degrade the mean-square-error (MSE) performance of the receivedconstellation signals at the input of the signal demapping and decodingblock. Furthermore, if a diversity and the maximum ratio combining (MRC)technique is employed at the receiver, the residual phase errors due toimperfect channel estimation in each branch will further degrade theoverall system performance because the MRC requires co-phase signalsfrom two branches of the receiver.

Residual Phase Error Estimation. The objective is to reduce the residualphase error in received constellation signals due to the pilot-basedchannel estimation. To reduce the effect of the channel phase estimationerror on transmitted symbols, the channel phase estimation error mustfirst be estimated and then removed from the received signals. What isdescribed herein is a novel technique for estimating the residual phaseerror, φ_(N), and utilizing it for such correction.

In Eq. 20, the received constellation symbol after the signal correctionin the transfer domain is represented as

$\quad\begin{matrix}\begin{matrix}{{\hat{X}}_{i} = {{\frac{1}{1 + \frac{\zeta}{\alpha }} \cdot {\mathbb{e}}^{{- {j\phi}}\; N} \cdot S_{i}} + S_{Ni}}} \\{= {{\frac{1}{1 + \frac{\zeta}{\alpha }} \cdot {\mathbb{e}}^{{- {j\phi}}\; N} \cdot S_{i}} + {\frac{{\hat{\alpha}}^{*}}{{\hat{\alpha}}^{2}} \cdot n_{i}}}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 22} \right)\end{matrix}$Using the similar method in deriving the Eq. 13, the Eq. 22 can besimplified as

$\begin{matrix}{{{\hat{X}}_{i} = {\left\lbrack {{\frac{1}{1 + \frac{\zeta}{\alpha }} \cdot {S_{i}}} + ɛ_{i}} \right\rbrack \cdot {\mathbb{e}}^{j{({{- \phi_{N}} + \phi_{i} + \phi_{ni}})}}}}{{i = 1},2,3,\ldots\mspace{14mu},{M - 1}}} & \left( {{Eq}.\mspace{14mu} 23} \right)\end{matrix}$where ε_(i), represents the effect of the second item in Eq. 22 on theamplitude of the ith transmitted symbol, S_(i), and is a random variableand is confined within the following range:

$\begin{matrix}{{\frac{1}{1 + \frac{\zeta}{\alpha }} \leq ɛ_{i} < \infty}{{i = 1},2,3,\ldots\mspace{14mu},{M - 1}}} & \left( {{Eq}.\mspace{14mu} 24} \right)\end{matrix}$and φ_(ni), is due to the second item in Eq. 22. It is a uniformlydistributed random phase variable within a small range and its mean iszero.

In simplifying Eq. 23, we used the expressionS _(i) =|S _(i) |e ^(jφ) ^(i) i=1, 2, 3, . . . , M−1  (Eq. 25)where φ_(i), is the phase of the ith transmitted information symbol. Thetotal phase of the received signal, {circumflex over (X)}_(i), is givenasΦ_(i)<φ_(N)+φ_(i)+φ_(ni) i=1, 2, 3, . . . , M−1  (Eq. 26)and can be calculated based onΦ_(i) =a tan 2(imag({circumflex over (X)} _(i)),real({circumflex over(X)} _(i))) i=1, 2 . . . , M−1  (Eq. 27)where a tan 2 is the four-quadrant inverse tangent and its output is inthe interval [−π, π]; imag is the complex imaginary part; and real isthe complex real part.

The first objective is to estimate the residual phase error, φ_(N), fromphases of the received signals in Eq. 26. It is found that the residualphase error, φ_(N), is a constant for all M−1 received symbol signals.The phase errors, φ_(ni) i=1, 2, 3, . . . , M−1, in Eq. 26 are due toadditive white Gaussian noise and are all random variables with a zeromean. These errors can be, for example, averaged out over M−1 receivedsignal phases.

In order to estimate φ_(N), it is important to know the informationphase, φ_(i), for each transmitted symbol, S_(i). In the embodimentdescribed, a hard-decision slicer is employed to find each transmittedsymbol with a fair accuracy based on the corresponding receivedconstellation signal. The output of the slicer is the estimate of thecorresponding transmitted symbol at the transmitter end. Due to noise,co-channel interference, and channel estimation errors, the output ofthe slicer is given as

$\quad\begin{matrix}\begin{matrix}{{\hat{S}}_{i} = {{Slicer}\left( {\hat{X}}_{i} \right)}} \\{= {{Slicer}\left\lbrack {{\frac{1}{1 + \frac{\zeta}{\alpha }} \cdot {\mathbb{e}}^{{j\phi}\; N} \cdot S_{i}} + {\frac{{\hat{\alpha}}^{*}}{{\hat{\alpha}}^{2}} \cdot n_{i}}} \right\rbrack}} \\{= \left\{ \begin{matrix}S_{i} & \left( {{Right}\mspace{14mu}{decision}} \right) \\S_{j\;} & {\left( {{Wrong}\mspace{14mu}{decision}} \right),{i \neq j}}\end{matrix} \right.}\end{matrix} & \left( {{Eq}.\mspace{14mu} 28} \right)\end{matrix}$where S_(i), and S_(j), are transmitting constellation symbols. Thecorresponding information phase estimate, φ, is given as

$\quad\begin{matrix}\begin{matrix}{{{\hat{\phi}}_{i} = {{a\;\tan\; 2\left( {{{imag}\left( {\hat{S}}_{i} \right)},{{real}\left( {\hat{S}}_{i} \right)}} \right)\mspace{25mu} i} = 1}},2,\ldots\mspace{14mu},{M - 1}} \\{= \left\{ \begin{matrix}\phi_{i} & \left( {{Right}\mspace{14mu}{decision}} \right) \\\phi_{j\;} & {\left( {{Wrong}\mspace{14mu}{decision}} \right),{i \neq j}}\end{matrix} \right.}\end{matrix} & \left( {{Eq}.\mspace{14mu} 29} \right)\end{matrix}$where, φ_(i); and φ_(j) are the phases of transmitted symbols, S_(i) andS_(j).

The symbol error is due to channel impairments and channel estimationerrors. If the channel is very bad, the symbol error rate will be veryhigh and therefore the slicer may not be reliable. In most situations,however, the symbol error rate is acceptable. For example, the symbolerror rate is likely to be less than 5*10⁻² when the slicer is employedin the embodiment described. That is, there may be one symbol errorevery 20 constellation symbols. Thus, for an OFDM-based system with theblock size of 20, there may be one symbol error every OFDM data block.If the symbol error rate is 10⁻², then there may be one symbol errorevery 5 OFDM data blocks. As apparent, the slicer can be used toestimate the transmitted information symbol with an acceptable accuracy.

If no symbol error occurs in the slicer, the resulting phase error isgiven as

$\quad\begin{matrix}{{{\Phi_{err}(i)} = {{\Phi_{i} - \phi_{i}}\mspace{65mu} = {{{- \phi_{N}} + {\phi_{ni}\mspace{14mu} i}} = 1}}},2,\ldots\mspace{14mu},{M - 1}} & \left( {{Eq}.\mspace{14mu} 30} \right)\end{matrix}$The estimate, {circumflex over (Φ)}_(N), of the residual phase error,φ_(N), due to channel impairments can be calculated by averaging thephase error in Eq. 30 over M−1 received symbols based on

$\quad\begin{matrix}\begin{matrix}{{\hat{\phi}}_{N} = {{- \frac{1}{M - 1}}{\sum\limits_{i = 1}^{M - 1}\;{\Phi_{err}(i)}}}} \\{= {{- \frac{1}{M - 1}}{\sum\limits_{i = 1}^{M - 1}\left( {{- \phi_{N}} + \phi_{ni}} \right)}}} \\{= {\phi_{N} - {\frac{1}{M - 1}{\sum\limits_{i = 1}^{M - 1}\phi_{ni}}}}}\end{matrix} & \left( {{Eq}.\mspace{14mu} 31} \right)\end{matrix}$Since φ_(ni), i=1, 2, 3, . . . , M−1, are random variables with zeromeans, the second item in Eq. 31 approaches zero when M>>1. As a result,the estimate of the residual phase error is{circumflex over (φ)}_(N)≅φ_(N) if M>>1  (Eq. 32)Assuming that there is one symbol error and the jth transmitted symbolS_(j) is sliced as S_(i)i≠j, in the nth OFDM block, then the total phaseerror for the jth received symbol is as follows:

$\begin{matrix}{\begin{matrix}{{\Phi_{err}(j)} = {\Phi_{j} - \phi_{j}}} \\{= {{- \phi_{N}} + \phi_{nj} + \left( {\phi_{j} - \phi_{i}} \right)}} \\{= {{- \phi_{N}} + \phi_{nj} + \Delta}}\end{matrix}{where}} & \left( {{Eq}.\mspace{14mu} 33} \right) \\{{\Delta = {\phi_{j} - {\phi_{i}\mspace{14mu} i}}},{j = 1},2,\ldots\mspace{14mu},{{M - {1\mspace{14mu}{and}\mspace{14mu} i}} \neq j}} & \left( {{Eq}.\mspace{14mu} 34} \right)\end{matrix}$

If Δ=0, the symbol error does not have any effect on the estimation ofthe residual phase error using. Eq. 31. Otherwise, we have|Δ|≧Δ_(min)  (Eq. 35)where Δ_(min) is the minimum phase difference between two constellationsymbols if both symbols do not have the same phase. For instance, for a16-QAM constellation, the Δ_(min)=π/8, while for the QPSK constellation,Δ_(min)=π/2.

Therefore, an incorrect hard-decision or a symbol error results ineither a large or a small phase error for that symbol. If the maximumand minimum values (i.e., largest of the absolute values) from M phaseerrors in Eq. 30 are removed, and the remaining phase errors areaveraged, the effect of a symbol error on the estimation of the residualphase error will be minimized. The estimate can be used to approximatethe real residual phase error as reflected by{circumflex over (φ)}_(N)≈φ_(N) if M>>1  (Eq. 36)

Statistically, if there are two symbol errors per OFDM data block, thefirst two maximums and minimums (i.e., largest magnitudes) from M phaseerrors are ignored. Since the size of cluster M is about 20, few symbolerrors do not significantly affect the estimation of the residual phaseerror. In fact, it is rare that there are even a few symbol errors perOFDM block.

Once the residual phase error due to the channel estimation isestimated, its effect on the received constellation signal is correctedor compensated. Since this estimation method utilizes the detectedsymbols, it may be referred to as the data-directed residual phase errorestimation (DD-RPEE) method. The correction or compensation method basedon the DDRPEE may be referred to as the data-directed residual phaseerror correction (DD-RPEC) method.

Phase Error Reduction. A residual phase error estimator and corrector,that is, the DD-RPEE and the DD-RPEC previously derived, and anOFDM-based wireless receiver having the DD-RPEE and DD-RPEC, aredepicted in FIG. 5. An alternative OFDM-based wireless receiver havingthe DD-RPEE and DD-RPEC to reduce channel phase estimation error isdepicted in FIG. 6. One or more processors may be utilized to performthe processes described, but preferably a single processor is utilizedsuch as a single digital signal processor (DSP) to execute theappropriate steps.

More particularly, FIG. 5 shows a schematic block diagram of receiverprocessing components 500 of a remote unit. Receiver processing.components 500 include a channel estimation process 502, a channelcompensation process 504, and a residual phase error (RPE) estimationprocess 506. Residual phase error estimation process 506 includes aphase calculation process 508 for channel-compensated data symbols, asymbol slicer 510, a phase calculation process 512 for informationsymbols, a subtractor process 514, a maximum value removal process 516,an averaging process 518, and a-signal correction process denoted at 520and 522.

An alternate embodiment in FIG. 6 shows receiver processing components600 which include a channel estimation process 602, a channelcompensation process 604, and a residual phase error (RPE) estimationprocess 606. Residual phase error estimation process 606 includes aphase calculation process 608 for channel-compensated data symbols, asymbol slicer 610, a phase calculation process 612 for informationsymbols, a subtractor process 614, a maximum value removal process 616,an averaging process 618, and a signal correction process denoted at620, 622, and 624.

The DD-RPEE and DD-RPEC will now be described in relation to theflowchart of FIG. 7 and in connection with FIG. 5. The signal is firstreceived (step 702 of FIG. 7 and point 550 of FIG. 5). Here, the nthblock of M received symbols, r(n) or r, is taken from outputs of themultiple access (FFT) block in the receiver at a time n. The nthreceived signal vector, r, is given in Eq. 5. Next, the fading channelgain is estimated (step 704 of FIG. 7 and channel estimation process 502of FIG. 5). Here, the pilot tone symbol, r_(P), in the nth receivedsignal vector, r, is used to estimate the fading channel gain,α=|α|e^(jφ). The channel estimate, {circumflex over (α)}=|{circumflexover (α)}|e^(jφ), is calculated based on Eq. 10. Next, the receivedsignal, r_(in), is corrected or compensated (step 706 of FIG. 7 andchannel compensation process 504 of FIG. 5). The nth receivedinformation-bearing data block of M−1 symbols, r_(in), was corrupted bythe fading channel gain and noise. Step 706 corrects or compensates thesignal vector, r_(in), with the channel estimate, {circumflex over(α)}=|{circumflex over (α)}|e^(jφ), from step 704, based on Eq. 16. Theoutput signal vector, {circumflex over (X)}_(in), is given in Eq. 16,and it contains M−1 compensated information-bearing tone symbols whichare corrupted by the channel estimation errors including channelresidual amplitude and phase errors and noise.

The “core” of the phase error estimation begins in the next step. Thephase of signal vector, {circumflex over (X)}_(in) is calculated (step708 of FIG. 7 and phase calculation process 508 of FIG. 5). Here, thesignal vector, {circumflex over (X)}_(in), has M−1 data symbols and thephase, φ_(i) i=1, 2, 3, . . . , M−1, of each symbol is calculated basedon Eq. 26. Next, the transmitted symbols are estimated (step 710 of FIG.7 and symbol slicer 510 of FIG. 5). In this step, a hard-decision ismade for each element of signal vector, {circumflex over (X)}_(in), toestimate its corresponding information symbol, X_(i)=S_(i) (where i=1,2, 3, . . . , M−1). The hard-decision is implemented by a correspondingconstellation slicer. If no decision error occurs, the output is thesymbol transmitted from the transmitter; otherwise, the output is anincorrect symbol. Next, the phases of each estimated information symbolare estimated (step 712 of FIG. 7 and phase calculation process 512 ofFIG. 5). Here, the phase of the estimated information symbol, Ŝ_(i)(where i=1, 2, 3, . . . , M−1), is calculated based on Eq. 29. Next, theinformation phase is subtracted from the total received signal phase(step 714 of FIG. 7 and subtractor process 514 of FIG. 5). For executionof this step, the total signal phase was given in step 708 and the phaseof its estimated information symbol was given in step 712. Thedifference, φ_(err)(i) i=1, 2, 3, . . . , M−1, between the total phaseof the received signal and the phase of its corresponding estimatedinformation symbol is calculated based on Eq. 28. If a symbol isdetected with an error, the resulting phase difference is relativelylarge.

Next, the largest magnitude phase error is removed (step 716 of FIG. 7and maximum value removal process 516 of FIG. 5). As previouslydescribed, the largest magnitude phase error corresponds to a symboldetection error. Removing the largest magnitude phase difference fromM−1 phase difference variables, φ_(err)(i) i=1, 2, 3, . . . , M−1, willresult in an unbiased estimate of phase error. Therefore, only M−2 phasedifference variables are left for next step processing. It is noted thatany suitable number of maximum values may be removed. Next, the phasedifferences are averaged (step 718 of FIG. 7 and averaging process 518of FIG. 5). There are a total of M−2 phase difference variables fromstep 716, and the average is performed over M−2 variables based on Eq.29. The mean or the output of averaging process 518 is the estimate ofthe residual phase error. Finally, the signal vector, {circumflex over(X)}_(in), is corrected or compensated (step 720 of FIG. 7 and blocks520 and 522 of FIG. 5). In FIG. 5, the residual phase error in eachelement of the signal vector, {circumflex over (X)}_(in), is removed bymultiplying the received signal with the estimated residual phase error.The output will be the “clear” signal.

The channel estimate may need to be corrected (step 722 of FIG. 7 andblock 622 of FIG. 6). For the alternative/extended version shown in FIG.6, the channel estimate, {circumflex over (α)}=|{circumflex over(α)}|e^(jφ), is first compensated with the estimated residual phaseerror, {circumflex over (φ)}, based on the following equation, and thenthe corrected channel estimate, {circumflex over (α)}, is used tocorrect or compensate (block 624 of FIG. 6) the received signal vector,{circumflex over (X)}_(in), by repeating step 720:ã={circumflex over (α)}·e ^(−j{circumflex over (φ)})  (Eq. 37)The received signal is then demodulated/decoded (step 724). Thecorrected received signal, based on the output of steps 720 and 722, isfed to demodulation and decoding blocks to retrieve transmittedinformation bits.

It should be readily apparent and understood that the foregoingdescription is only illustrative of the invention and in particularprovides preferred embodiments thereof. Various alternatives andmodifications can be devised by those skilled in the art withoutdeparting from the true spirit and scope of the invention. Accordingly,the present invention is intended to embrace all such alternatives,modifications, and variations which fall within the scope of theappended claims.

1. An apparatus comprising: a residual phase error estimator configuredto estimate a residual phase error at least partially based on aplurality of phases of a first channel-compensated received signal and aplurality of phases of a sliced version of the first channel-compensatedreceived signal and configured to correct a channel estimate at leastpartially based on the residual phase error estimate, to therebygenerate a corrected channel estimate; and a channel compensatorconfigured to generate a second channel-compensated received signal atleast partially based on a received signal and the corrected channelestimate.
 2. The apparatus, as recited in claim 1, further comprising: achannel estimator configured to generate a channel estimate at leastpartially based on the received signal; and a first channel compensatorconfigured to generate the first channel-compensated signal at leastpartially based on the received signal and the channel estimate.
 3. Theapparatus, as recited in claim 2, wherein the channel estimate isgenerated using a pilot tone symbol received in an OFDM communicationsignal and a previously known pilot tone symbol.
 4. The apparatus, asrecited in claim 1, wherein the residual phase error estimatorcomprises: a first phase calculator configured to determine theplurality of phases of the first channel-compensated signal; a slicerconfigured to generate the sliced version of the firstchannel-compensated received signal; a second phase calculatorconfigured to determine the plurality of phases of the sliced version ofthe first channel-compensated received signal; and an error calculatorconfigured to generate a residual phase error at least partially basedon the plurality of phases of the first channel-compensated receivedsignal and the plurality of phases of the sliced version of the firstchannel-compensated received signal.
 5. The apparatus, as recited inclaim 4, wherein the error calculator comprises: a difference calculatorconfigured to generate a plurality of phase differences corresponding todifferences between corresponding phases of the plurality of phases ofthe first channel-compensated received signal and the plurality ofphases of the sliced version of the first channel-compensated receivedsignal; a maximum value remover configured to identify a subset of theplurality of phase differences and to omit from the subset one or moreof the largest magnitudes of the plurality of phase differences; and anaverager configured to generate an average phase difference based on thesubset of the plurality of phase differences.
 6. A method for use inorthogonal frequency division multiplexed (OFDM) communications, themethod comprising: estimating a residual phase error at least partiallybased on a plurality of phases of a first channel-compensated receivedsignal and a plurality of phases of a sliced version of the firstchannel-compensated received signal to thereby generate a residual phaseerror estimate; and generating a second channel-compensated receivedsignal at least partially based on the received signal and a correctedchannel estimate, the corrected channel estimate being at leastpartially based on the residual phase error estimate.
 7. The method, asrecited in claim 6, further comprising: generating a channel estimate;and generating a first compensated received signal at least partiallybased on the received signal and the channel estimate to therebygenerate the first channel-compensated received signal.
 8. The method,as recited in claim 7, wherein the channel estimate is generated using apilot tone symbol received in an OFDM communication signal and apreviously known pilot tone symbol.
 9. The method, as recited in claim6, wherein the estimating the residual phase error comprises:determining the plurality of phases of the first channel-compensatedreceived signal; generating the sliced version of the firstchannel-compensated received signal; determining the plurality of phasesof the sliced version of the channel-compensated received signal; andgenerating the residual phase error estimate at least partially based onthe plurality of phases of the first channel-compensated received signaland the plurality of phases of the sliced version of the firstchannel-compensated received signal.
 10. The method, as recited in claim6, wherein the generating the residual phase error estimate comprises:calculating a plurality of phase differences corresponding todifferences between corresponding phases of the plurality of phases ofthe first channel-compensated received signal and the plurality ofphases of the sliced version of the first channel-compensated receivedsignal; identifying a subset of the plurality of phase differences andomitting from the subset one or more of the largest magnitudes of theplurality of phase differences; and generating an average phasedifference based on the subset of the plurality of phase differences.11. An apparatus comprising: means for estimating residual phase errordue to channel estimation, wherein the means for estimating comprises:means for generating a residual phase error at least partially based ona plurality of phases of a channel-compensated received signal and aplurality of phases of a sliced version of the channel-compensatedreceived signal; and means for compensating a received constellationsignal based on the estimated residual phase error due to channelestimation.
 12. The method, as recited in claim 11, wherein the meansfor estimating comprises: means for determining a plurality of phases ofthe channel-compensated received signal; means for generating the slicedversion of the channel-compensated received signal; and means fordetermining the plurality of phases of the sliced version of thechannel-compensated received signal.